Option Pricing and Volatility Modeling with Python: Implementing Black-Scholes and GARCH Models

The Python Lab
6 min readJun 10, 2023

Option Pricing is a common problem in Finance that requires pricing financial options. Volatility Modeling is another important concept that focuses on predicting the magnitude of price changes in the stock market. Python is a powerful tool that can be used to model these concepts.

In this tutorial, we will explore how to implement two popular models for Option Pricing and Volatility Modeling in Python: the Black-Scholes Model and the GARCH Model. You will learn how to apply the Black-Scholes model to value European call and put options. The GARCH Model will be used to estimate volatility for stock prices.

To follow along with this tutorial, you should have a basic understanding of Python and finance concepts.

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Understanding the Black-Scholes Model

The Black-Scholes Model is a popular method for pricing European-style options. It is used to determine a fair price for a call or put option based on several factors, including the strike price, time to expiration, underlying asset price, risk-free rate, and expected volatility. The Black-Scholes formula is a partial differential equation where the option price is the unknown function. This formula can be solved using numerical techniques…



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